In a fractal distribution one expects to find persistent scale-invariant
fluctuations around the average behavior, which do not decay with apparent
magnitude. On the other hand, in an homogeneous distribution, on large
enough scales, the relative variance of the counts of galaxies should
decrease exponentially with the apparent magnitude.

Personally I think that observational data provides us with no evidence that
the universe is either homogeneous and isotropic, or monofractal or
multifractal.